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Logic systems for approximate reasoning: via rough sets and topology

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Methodologies for Intelligent Systems (ISMIS 1994)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 869))

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Abstract

Mathematicians formalized the approximation in terms of topology. In this paper a new family of logic systems for approximate reasoning, called Near Logic, is proposed; their semantics are rested on the notion of neighborhood system-a building block of topology. Somewhat surprisingly, the axiom schema of the Near Logic is that of the modal logic S4. This generalizes the fact that the axiom schema of Rough Logic is S5. The agreement in geometric and modalic considerations seems indicate that the proposed approach must have captured some intrinsic meaning of the approximate reasoning. Neighborhood Systems are very general approximation, so Near Logic can be regarded as a small step toward the formalization what Hao Wang called ”approximate proof” three decades ago.

On leave from Jiangxi University Nan-Chang, Jiangxi, P.R. China

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Zbigniew W. Raś Maria Zemankova

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© 1994 Springer-Verlag Berlin Heidelberg

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Lin, T.Y., Liu, Q., Yao, Y.Y. (1994). Logic systems for approximate reasoning: via rough sets and topology. In: Raś, Z.W., Zemankova, M. (eds) Methodologies for Intelligent Systems. ISMIS 1994. Lecture Notes in Computer Science, vol 869. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58495-1_7

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  • DOI: https://doi.org/10.1007/3-540-58495-1_7

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58495-7

  • Online ISBN: 978-3-540-49010-4

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